Theorems · Theorem · field theory
Polynomial.Sequence.span_degreeLT
∀ {R : Type u_1} [inst : Ring R] (S : Polynomial.Sequence R) {m : ℕ},
(∀ i < m, IsUnit (↑S i).leadingCoeff) → Submodule.span R (↑S '' Set.Iio m) = Polynomial.degreeLT R mThe first m polynomials of a polynomial sequence span all polynomials of degree < m if their
leading coefficients are units.
- Defined in
- Mathlib.Algebra.Polynomial.Sequence
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites54
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- Polynomialstatement and proof · cited by 5,681
- Set.imagestatement and proof · cited by 5,609
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Nontrivialproof · cited by 2,416
- zero_addproof · cited by 2,366
- le_reflproof · cited by 2,061
- IsUnitstatement and proof · cited by 1,602
- Submodule.spanstatement and proof · cited by 1,504
- WithBotproof · cited by 1,498
Cited by3
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.integral_eq_sumZeroesproof · cited by 0
- Polynomial.Sequence.spanproof · cited by 0
- Polynomial.Sequence.span_degreeLEproof · cited by 0